This is speculation on my part. In Toole's book, he quotes Haas: "The human auditory system combines the information contained in a set of
reduplicated sound sequences and hears them as though they were a single entity, provided (a) that these sequences are
reasonably similar in their spectral and temporal patterns and (b) that most of them arrive within a time interval of about 40 ms following the arrival of the first member of the set." Also, "Within the precedence effect fusion interval, there is no masking—all of the reflected (delayed) sounds are
audible, making their contributions to timbre and loudness, but the early reflections simply are not heard as spatially separate events. They are perceived as coming from the direction of the first sound; this, and only this, is the essence of the “fusion.” The widely held belief that there is a “Haas fusion zone,” approximately the first 20 ms after the direct sound, within which everything gets innocently combined, is simply untrue."
He then goes on to show a series of threshold curves showing the level of a simulated reflection on the Y-axis and the relative delay on the X-axis, suggesting that lower level reflections present later may not be detectable or else may contribute to image shift or spreading, but are still not heard as separate events, hence fusion is still occurring. Once delayed reflections reached a certain threshold, then the precedence effect broke down, and these individual reflections were heard as separate events or "images."
Here are two such graphs:
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Towards the end of that chapter, he references an experiment that he and Olive did where they low-passed the simulated reflection below 500 Hz, which actually changed the level of detection:
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He writes "The amplitudes are rather similar, although the low-pass filtered version is a little higher, which seems to make sense considering
that slightly over 5 octaves of the audible spectrum have been removed from the signal. Recall that these signals have been adjusted to produce the same subjective effect—a threshold detection—and it would be logical for a reduced bandwidth signal to be higher in level...The message is that we need to know the spectrum level of reflections to be able to gauge their relative audible effects."
I thought this might suggest that the difference in the threshold detection in terms of relative level for a distorted reflection might be reflected (sorry, no pun intended) in the precedence-effect fusion interval, but I was asking it as a question.